President Reagan announced yesterday that he will meet with Soviet Foreign Minister Andrei A. Gromyko Sept. 28 to discuss arms control and U.S.-Soviet relations in a session that Republicans hope will help to neutralize the war-and-peace issue in the presidential campaign.

Stressing his desire to convince Gromyko that "the United States means no harm" and that "one of my highest priorities is finding ways to reduce the levels of arms," Reagan underscored the political value of the announcement by making it himself at the White House.

Administration officials said they did not expect major substantive progress from the meeting; Vice President Bush said, "I'm not expecting the world to come out of it."

But Reagan political strategists said the meeting could provide a reelection bonus in light of polls showing that American voters fault Reagan for not having any talks with Soviet leaders during his presidency, although they support his hard-line stance toward Moscow. Reagan's recent joke about bombing the Soviets produced a wave of unease reflected in his campaign polls.

Democratic presidential nominee Walter F. Mondale, campaigning in the Midwest, said it was "pathetic" that Reagan's first scheduled encounter with a top-level Soviet leader had not been arranged until Reagan was in the midst of a reelection drive. Details on Page A9.

The president has never met Gromyko and the session comes at a time when U.S. officials believe the foreign minister has assumed ever-increasing responsibility for Soviet foreign policy. Gromyko, who is to attend the opening session of the U.N. General Assembly, will meet first in New York with Secretary of State George P. Shultz before seeing Reagan at the White House. Reagan is to address the United Nations Sept. 24.

Questioned yesterday whether "some people might consider this a political ploy" to answer Mondale's criticism, Reagan told reporters, "I would answer that the facts would belie any such supposition. The fact is we have proposed meetings with the Soviet Union on a number of occasions . . . . We have not retreated from any meetings with them."

Reagan was referring to the breakdown in proposed negotiations on space weapons in Vienna this month and the Soviet walkout from separate talks on limiting intermediate-range nuclear missiles in Europe and intercontinental missiles.

The president said he was not worried that Gromyko might attempt to use the meeting to embarrass him but declined to comment on Soviet motivations for beginning talks now. Reagan said the meeting would be "confidential" and the only agenda item he identified was arms control.

"The most important thing is what understanding I can reach with Foreign Minister Gromyko to maybe convince him the United States means no harm," Reagan said. He added that "a better understanding between our two governments maybe should precede any resumption of dealings on specifics."

Reagan said he hoped the meeting could ease "any suspicion or hostility" by the Soviets, and repeated his campaign theme that "the most important thing to begin with is to see if we cannot lessen this threat hanging over the world" of nuclear weapons.

"We've always said it was the Russians, not Reagan, who wasn't willing to sit down and talk," said Reagan campaign spokesman James Lake. "Anything that contributes to the image of Reagan as a man of peace who is willing to talk directly to the Russians about arms control serves the cause of the president."

Reagan said he would not "hazard a guess" about Gromyko's current standing in the Soviet leadership and added that "I've been facing a problem that no other president has faced and that is the great turnover" in Soviet leadership.

The president said he is not concerned that a report on Soviet violations of past arms control treaties -- recently sent to the White House and due to be submitted to Congress next week -- could sour the atmosphere for the Gromyko meeting. "This is not some action by us or aimed at the Soviet Union," Reagan said.

Reagan also renewed his criticism of Mondale's deficit-reduction plan but refused to specify spending cuts he would make.

Responding to criticism that he has been inaccessible, Reagan told reporters that he would have more news conferences but offered no specifics.